Preheat oven to 350 degrees F. Scrub beets, trim root ends, and cut off stems and greens. Reserve and refrigerate half the greens. Brush beets with olive oil and wrap each individually in foil. Place in a roasting pan and roast 45 minutes to 1 hour, until beets can be pierced with a knife. Allow to cool at room temperature 1 hour, until beets are still warm but cool enough to handle. Unwrap the foil and gently rub the skins from the beets; they should slip off easily. Cut beets into ¼-inch slices and place in a mixing bowl. Heat vinegars and sugar in a saucepan until the sugar has dissolved, then pour mixture over beets. Carefully turn the beets with a rubber spatula to coat. Drizzle oil over beets; add salt and pepper to taste. Chill overnight.
To serve, wash beet greens and trim stems. Chiffonade the greens (stack and roll the leaves, then slice thinly), and place them in a mixing bowl. Turn beets several times with a spatula, then pour off excess juices over beet greens and toss. Arrange bed of greens on a platter; top with beets.